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Find the antilogarithms of the following numbers: a) 0.3760 b) 0.7783 c) 1.6415 d) 1.1127 e) 1.9364 f) 2.8579 g) 2.8835 h) 3.5104 i) 1.8056 j) 0.5467

Mathematics

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Here are the numbers whose logarithms are given:

  • The antilogarithm of a number xx is 10x10^x.
  • For logarithms with a bar notation, e.g., 1ˉ.8056\bar{1}.8056, it means −1+0.8056-1 + 0.8056.

Part a· 1 step

For 0.3760

  1. Calculate the antilogarithm.

    100.3760≈2.37710^{0.3760} \approx 2.377

    The number is 2.377\boxed{2.377}.

Part b· 1 step

For 0.7783

  1. Calculate the antilogarithm.

    100.7783≈6.00310^{0.7783} \approx 6.003

    The number is 6.003\boxed{6.003}.

Part c· 1 step

For 1.6415

  1. Calculate the antilogarithm.

    101.6415≈43.8010^{1.6415} \approx 43.80

    The number is 43.80\boxed{43.80}.

Part d· 1 step

For 1.1127

  1. Calculate the antilogarithm.

    101.1127≈13.0510^{1.1127} \approx 13.05

    The number is 13.05\boxed{13.05}.

Part e· 1 step

For 1.9364

  1. Calculate the antilogarithm.

    101.9364≈86.3910^{1.9364} \approx 86.39

    The number is 86.39\boxed{86.39}.

Part f· 1 step

For 2.8579

  1. Calculate the antilogarithm.

    102.8579≈721.010^{2.8579} \approx 721.0

    The number is 721.0\boxed{721.0}.

Part g· 1 step

For 2.8835

  1. Calculate the antilogarithm.

    102.8835≈764.710^{2.8835} \approx 764.7

    The number is 764.7\boxed{764.7}.

Part h· 1 step

For 3.5104

  1. Calculate the antilogarithm.

    103.5104≈323910^{3.5104} \approx 3239

    The number is 3239\boxed{3239}.

Part h(i)· 8 steps

For 1ˉ.8056\bar{1}.8056

  1. Rewrite the logarithm.

    1ˉ.8056=−1+0.8056\bar{1}.8056 = -1 + 0.8056
  2. Calculate the antilogarithm.

    10−1+0.8056=100.8056×10−1≈6.392×10−1=0.639210^{-1 + 0.8056} = 10^{0.8056} \times 10^{-1} \approx 6.392 \times 10^{-1} = 0.6392

    The number is 0.6392\boxed{0.6392}.

    j) For 1ˉ.7194\bar{1}.7194:

  3. Rewrite the logarithm.

    1ˉ.7194=−1+0.7194\bar{1}.7194 = -1 + 0.7194
  4. Calculate the antilogarithm.

    10−1+0.7194=100.7194×10−1≈5.241×10−1=0.524110^{-1 + 0.7194} = 10^{0.7194} \times 10^{-1} \approx 5.241 \times 10^{-1} = 0.5241

    The number is 0.5241\boxed{0.5241}.

    k) For 2ˉ.5518\bar{2}.5518:

  5. Rewrite the logarithm.

    2ˉ.5518=−2+0.5518\bar{2}.5518 = -2 + 0.5518
  6. Calculate the antilogarithm.

    10−2+0.5518=100.5518×10−2≈3.563×10−2=0.0356310^{-2 + 0.5518} = 10^{0.5518} \times 10^{-2} \approx 3.563 \times 10^{-2} = 0.03563

    The number is 0.03563\boxed{0.03563}.

    l) For 3ˉ.2052\bar{3}.2052:

  7. Rewrite the logarithm.

    3ˉ.2052=−3+0.2052\bar{3}.2052 = -3 + 0.2052
  8. Calculate the antilogarithm.

    10−3+0.2052=100.2052×10−3≈1.604×10−3=0.00160410^{-3 + 0.2052} = 10^{0.2052} \times 10^{-3} \approx 1.604 \times 10^{-3} = 0.001604

    The number is 0.001604\boxed{0.001604}.

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